"The number of children on the move is staggering, an indication of how desperate the situation has become," said Afshan Khan, UNICEF's regional director for Europe and Central Asia. "Children are leaving behind everything they know in search of safety. It is heartbreaking".
UNHCR, the UN refugee agency, now puts the total number of refugees at 2.3 million and internally displaced people at 1.9 million.
UNICEF has so far delivered six truckloads of nearly 70 tonnes of supplies to Ukraine, including personal protective equipment and medical, surgical and obstetric kits. All the material will be delivered to 22 hospitals in five different war-affected areas of Ukraine to help 20,000 children and mothers.
Across the border, the United Nations Children's Fund sent three trucks from Copenhagen - UNICEF's warehouse in Europe and the world's largest humanitarian hub. The trucks were carrying essential supplies, including early childhood development kits, recreational kits and hygiene kits. The supplies have already arrived in Poland.
Meanwhile, the UN Refugee Agency tells us that as of 9 March it had delivered 85 metric tonnes of humanitarian aid to reception and transit centres in Vinnytsia, central Ukraine, which is hosting people who have fled hostilities further east.
For its part, the World Food Programme (WFP) has expressed deep concern about the impact of the conflict on the ability of Ukrainians to feed themselves, especially families trapped in besieged areas.
The UN agency plans to assist up to 3.1 million people. Its priority is to supply Ukrainian cities with bulk food, bread and food rations.
With food aid shipments arriving every day, the Programme is in a race against time to stockpile food in areas where fighting is expected to break out.
Its sister agency in Rome, the UN Food and Agriculture Organisation (FAO), warns that the next few weeks will be critical, as farmers will have to prepare the land for vegetable planting in mid-March.
It also said farmers must start preparing land for planting wheat, barley, maize and sunflowers. The FAO stressed that everything possible must be done to protect crops and livestock, and I think we all know what a vital role the Ukrainian grain market plays for the rest of the world.
The World Health Organisation said it has so far delivered 81 metric tonnes of health supplies and is establishing a stockpile for health facilities across Ukraine. The WHO has also released $10.2 million from the Contingency Fund and deployed staff to care for refugees.
Despite all this assistance provided by the UN in collaboration with organisations operating inside and outside Ukraine, the humanitarian situation continues to deteriorate at an "alarming rate", the UN spokesperson said.
"So far, together with our partners, we have provided some form of humanitarian assistance to more than 500,000 people in Ukraine, including food, shelter, blankets and life-saving medical supplies. If humanitarian access is guaranteed, we are ready to reach much higher numbers given the scope and scale of humanitarian operations currently being deployed," added Stephane Dujarric.
So far, the Ukraine 2022 Flash Appeal has received $109 million, representing 9.6 per cent of the UN Secretary-General's 1 March appeal for $1.1 billion for a three-month period for humanitarian response inside Ukraine.
As of midnight Wednesday, the Human Rights Office had verified that 549 civilians had been killed and 957 wounded across Ukraine, although the real figure is much higher, the UN spokesman said.
He also explained that the UN has no information that the shelled Mariupol hospital was used for other purposes, as the Russian authorities claim.
Asked about Russia's allegations that there were no patients in the hospital, but "Ukrainian nationalists", the UN spokesman said the UN has no such information.
"We have spoken to our colleagues in the Human Rights Office who are on the ground. The team has verified and documented what they describe as indiscriminate shelling of a hospital that was treating women and children," Stephane Dujarric said.
The UN also has no information on the use of chemical or biological weapons in Ukraine, which would be "a serious violation of international law".
The spokesman also confirmed that Ukraine has withdrawn its 308 peacekeepers to return to the country.